CN104459667A

CN104459667A - Sparse array DOA estimation method based on CLEAN

Info

Publication number: CN104459667A
Application number: CN201410720772.2A
Authority: CN
Inventors: 杨刚; 袁子乔; 付学斌; 王亚军; 赵博
Original assignee: Xian Electronic Engineering Research Institute
Current assignee: Xian Electronic Engineering Research Institute
Priority date: 2014-12-01
Filing date: 2014-12-01
Publication date: 2015-03-25
Anticipated expiration: 2034-12-01
Also published as: CN104459667B

Abstract

The invention relates to a sparse array DOA estimation method based on CLEAN. The sparse array DOA estimation method based on CLEAN comprises the following steps that the number of targets is calculated according to the MDL rule; an amplitude square accumulation result of wave beams formed by all snapshot data is calculated; the calculation result is searched for the number of the wave beam corresponding to the maximum value; an accurate number of the wave beam is calculated through an equisignal angle measurement method; a target angle is calculated; whether all signals are detected or not is judged; detected target responses are removed through the CLEAN concept, and then iteration is conducted. By the adoption of the sparse array DOA estimation method based on CLEAN, the influence of action of a strong target and a high sidelobe on weak target angle estimation is well restrained, and a high angular accuracy is achieved; in addition, the consumed time is short, and time consumption is not sensitive to the number of array elements.

Description

Sparse array DOA estimation method based on CLEAN

Technical Field

The invention belongs to the technical field of radar signal processing, and particularly relates to a sparse array DOA estimation method based on CLEAN.

Background

In radar and communication systems, array antennas are used in an extremely wide variety of applications. To date, evenly spaced antennas are one of the simplest and most widely used array antennas. However, the possibility of grating lobes exists in the uniformly spaced antenna arrays, and in order to avoid the grating lobes, the spacing of the antenna arrays is usually required to be not more than half the wavelength. Therefore, if a high angular resolution is desired, a large number of elements are required, which not only increases the cost of the antenna, but also generates a large amount of data that increases the burden on the digital signal processing system.

And (3) carrying out sparsification treatment on the uniformly distributed array, namely randomly removing some array elements from the uniform array, so that the array elements are not regularly arranged any more to obtain the sparse array. The sparse array can effectively inhibit the occurrence of grating lobes and improve the angular resolution, but the peak side lobe and the mean side lobe of the sparse array are high, the response of the interaction of a strong target and the high side lobe is possibly greater than that of a weak target, and the probability of false targets is high.

Direction of Arrival (DOA) estimation is always one of the hot spots in the array signal processing field, and accurate DOA estimation is crucial to subsequent processing. Current research on DOA estimation algorithms focuses mainly on two excellent algorithms, MUSIC and ESPRIT.

The music (multiple Signal classification) algorithm has good resolution, but the algorithm needs to perform spectral peak search at all possible angles, the operation amount is extremely large, and the angle measurement precision is related to the interval of the selected search angle. Root-MUSIC is proposed on the basis of MUSIC, and a closed-form solution is directly obtained without performing spectral peak search. However, the Root-MUSIC algorithm has a strategy of solving the Root of a equation, and the time for solving the Root of the equation is increased rapidly along with the increase of the number of array elements, so that the Root-MUSIC increases the time burden when the number of array elements is large.

Disclosure of Invention

Technical problem to be solved

In order to avoid the defects of the prior art, the invention provides a sparse array DOA estimation method based on CLEAN, which solves the problem that when strong and weak targets coexist, the response corresponding to a false target generated by the interaction of the strong target and the high side lobe of the sparse array is larger than the response of the weak target.

Technical scheme

A sparse array DOA estimation method based on CLEAN is characterized by comprising the following steps:

step 1: calculating the number of targets in the sparse array signal of CLEAN by using a minimum description length MDL rule;

step 2: t is>When 0, calculating the square accumulation result of the amplitude of all the snapshot data formed beamsOtherwise, ending the calculation process; wherein: y is_sFor the s-th snapshot data x_sFormation using FFTBeam data of y_s＝FFT(x_s) (ii) a L is the number of fast beats;

and step 3: searching a beam number corresponding to the maximum value in the amplitude square accumulation result P;

and 4, step 4: calculating 'precise beam number' p by using equal signal angle measurement method_t，

Wherein p is₁Is the beam number corresponding to the maximum value in P, P₂The wave beam number is the second largest value, k is the amplitude comparison angle slope corresponding to the array, sign is the sign bit;

the above-mentioned

<math> <mrow> <mi>sign</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mo>-</mo> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo><</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

And 5: the target angle is calculated and the target angle is calculated,

wherein, λ is wavelength, d is array element interval, and M is FFT point number;

step 6: and (5) clearing the detected target response by applying a CLEAN idea, reducing the T value by one, and turning to the step 2 for iteration.

The sparse array is formed by randomly removing some array elements in a uniformly spaced array by using an array A_rrAnd the element corresponding to the removed array element is 0, and the element corresponding to the reserved array element is 1.

The application of CLEAN idea to clear the detected target response is: approximating the amplitude square accumulation result P of all the snapshot data formed beams calculated in the step 2 to the amplitude square accumulation of one snapshot data formed beam, and firstly solving a target T_mCorresponding amplitude

Wherein,P_m-1as a result of the (m) -1) th iteration, z_mIs P_m-1The beam number, theta, corresponding to the medium maximum value_mIs a step (f)

Calculated target T_mN is the number of array elements, k is 2 pi/λ;

at P_m-1Clearing the target T_mResponse to (2)

Advantageous effects

The invention provides a sparse array DOA estimation method based on CLEAN, which comprises the following steps: (a) calculating a target number using a Minimum Description Length (MDL) criterion; (b) calculating the amplitude square accumulation result of all snapshot data formed wave beams; (c) searching a beam number corresponding to the maximum value in the calculation result; (d) calculating 'accurate beam number' by using an equal signal angle measurement method; (e) calculating a target angle; (f) judging whether all signals are detected, if so, ending, otherwise, turning to (g); (g) and (c) clearing the detected target response by applying a CLEAN idea, and turning to (c) for iteration. The method can well inhibit the influence of strong target and high side lobe effect results on the estimation of the weak target angle, achieves high angle measurement precision, and is short in time consumption and insensitive to array element number.

According to the method, the influence of strong signals on weak signal detection can be eliminated by utilizing the CLEAN idea, and the algorithm is simple in calculation, so that the direction of arrival of the sparse array can be quickly and accurately estimated under the condition that the strong signals and the weak signals coexist.

Drawings

In all figures FAC represents the process of the invention, RM represents the Root-MUSIC process,

FIG. 1 is a flow chart showing the steps of the method of the present invention;

fig. 2 is a schematic diagram showing a directional diagram comparison of a sparse array (shown by SA in the figure) having an array element pitch of 0.5909 λ (λ is wavelength) and a one-dimensional uniform line array (shown by ULA in the figure) having an array element pitch of 0.5 λ in the case where the number of array elements is all 28.

FIG. 3 is a graph of the time comparison of the example method and the Root-MUSIC method with respect to the number of array elements.

FIG. 4 is an exemplary graph of two targets (one SNR of 20dB at an angle of 10 DEG; and the other SNR of 40dB at an angle of 30 DEG) for the method of this example, where (a) is the initial response plot, (b) is the response plot for the strong target, and (c) is the response plot resulting from the removal of (b) from (a).

FIG. 5 is a graph comparing the mean-squared error Root (RSME) against SNR for the method of this example and the Root-MUSIC method, for a target number of 2, for target angles of 10 and 30, respectively, for equal SNR for both targets, varying from 10dB to 70dB, and for a 1dB separation.

FIG. 6 is a graph showing the comparison of the performance of the method of this example with that of the Root-MUSIC method when the two targets have the same SNR (both 20dB) and the incident angles are relatively close (one of the targets is fixed at 20 degrees and the other target is varied from 20.15 degrees to 26 degrees with a spacing of 0.1 degrees), where (a) is an RMSE comparison plot and (b) is an angle comparison plot (the solid blue (angle-1) and the dotted line (angle-2) indicate the true angles of the two targets and the red and green sublists indicate the angle values found by FAC and RM)).

FIG. 7 is a graph showing the comparison of the performance of the method of this example and the Root-MUSIC method when the incident angles are relatively close when the SNR of the two targets are different (target 1 is 20dB and target 2 is 25dB), wherein target 1 is fixed at 20 DEG, target 2 is changed from 20.15 DEG to 26 DEG at an interval of 0.1 DEG, and (a) is an RMSE comparison chart, (b) is an angle comparison chart (the solid blue line (angle-1) and the broken line (angle-2) indicate the true angles of the two targets, and the red and green sublists indicate the angle values obtained by FAC and RM)

Detailed Description

The invention will now be further described with reference to the following examples and drawings:

the present invention is described by taking a one-dimensional array as an example.

For a one-dimensional linear array antenna composed of N elements, a sparse array can be obtained by randomly removing some elements. For convenience of description, a one-dimensional array A containing N elements is used_rrAnd representing a sparse array, wherein the element corresponding to the removed array element is 0, and the element corresponding to the reserved array element is 1. Assuming that the array element spacing is d, there are p incident targets with directions of theta_i(i-1, … p), and the noise received by each array element is zero-mean white gaussian noise. The received signal can be expressed as:

X＝(AS+N)·A_rr(1) in the formula, X is sampling data, S is a target vector, N is a noise vector, and a is a steering vector matrix, specifically:

A＝[a(θ₁)a(θ₂)…a(θ_p)](2) wherein a (θ)_i) A steering vector of the ith signal is specifically:

wherein k is 2 pi/lambda, and d is the array element spacing.

Now referring to fig. 1, a sparse array direction of arrival estimation method according to the present invention will be described

The method of the invention firstly needs to judge the number of targets. The accurate determination of the number of targets is important for DOA estimation, false targets can occur if the number of targets is selected to be too large, and targets can be missed if the number of targets is selected to be too small. As shown in fig. 1, in step S101, the Minimum Description Length (MDL) criterion is used in the present algorithm to calculate the target number T.

When forming wave beams, the sampled data of each array element is weighted and summed to obtain array output (4)

y＝W^HX＝W^H{(AS+N)·A_rr} (4) wherein W ═ W₁,W₂,…W_N]^TAnd the weight value is corresponding to each array element. When W is a (theta)_i) The beam will be directed at theta_iAnd (4) direction.

At this time, the process of the present invention,

if the quantization is performed according to equation (6),

then equation (5) becomes the DFT expression of x (t), and in practice, it is often implemented by FFT. Therefore, M-point FFT is performed on the sampled values obtained by the array to obtain M pieces of received beam data, and the relationship between each beam number and the corresponding beam pointing angle is shown in formula (6).

In step S102, judging whether T is larger than zero, if so, performing step S103, otherwise, ending the calculation process

In step S103, the S-th snapshot data is assumed to be x_sThen the beamforming result is: y is_s＝FFT(x_s). For the data with the fast beat number L, the obtained accumulation result of the square of the amplitude of the beam formed by all the fast beat data is as follows:

the difference to sum beam ratio between the two beams formed by the FFT is approximately proportional to the deviation of the target equal signal axis, and similarly, the amplitudes of the two beams are squared and then summed with the beam Σ and the difference beam Δ, Δ/Σ still being proportional to the deviation of the target from the equal signal axis. Therefore, when the accumulation result of each beam is obtained by equation (7), the ratio of the difference beam to the sum beam of two adjacent beams in P is linearly related to the signal axis such as the target deviation.

In step S104, find out the beam number P corresponding to the maximum value in P₁And the next largest value of the beam number p corresponding to the target₂。

In step S105, the "precise beam number" p corresponding to the target is obtained by using equation (9)_t。

K is the amplitude comparison angle slope corresponding to the array, is related to the specific array, utilizes the formula (5) to obtain the multi-beam response y, and then takes P ═ y²A 1 is to p₁And p₂Selecting any adjacent value of 0 … M-1, and adding p_tIs taken as p₁And p₂The value between k can be obtained by equation (9). sign is a sign bit, and the values are as follows:

<math> <mrow> <mi>sign</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mo>-</mo> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo><</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

in step S106, the angle corresponding to the target is obtained by equation (6):

<math> <mrow> <mi>θ</mi> <mo>=</mo> <mi>arcsin</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>t</mi> </msub> <mi>λ</mi> </mrow> <mi>Md</mi> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

since the side lobe of the sparse array is relatively high, the value of the generated false target in P is likely to be larger than the value of the real weak target in P, so that the maximum value point in P is likely to correspond to the false target. Therefore, when there are T targets found by the MDL, the maximum T maximum points in P are considered as incorrect targets.

In step S107, in order to suppress the influence of high side lobes, the idea of CLEAN is applied, and after each target is obtained, the response of the target is cleared in the calculation result. The precise method is to eliminate the influence of the target at each snapshot, but the algorithm complexity is very high, and the system requirement cannot be met in the occasion with high real-time requirement. Through simulation experiments, the result obtained by only one clearing operation is very close to the result obtained by one clearing operation per snapshot by regarding the calculation results (namely P) of all snapshots as the calculation result of one snapshot. Suppose a target T_mAt P_m-1(result of m-1 iteration) with a corresponding maximum beam number of z_mThe angle obtained by the formula (11) is θ_mThen the amplitude of the target is:

at P_m-1Clearing the target T_mAfter the response of (c), we get:

after step S107 is executed, the process proceeds to step S102 to iterate.

To illustrate the effectiveness of the method of the present invention, simulation experiments comparing the method of the present invention with the Root-MUSIC method are performed below. In the subsequent context of the present invention, FAC stands for the method of the present invention and RM for the Root-MUSIC method.

Without loss of generality, we chose to use sparse array A_rr＝[1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 10 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 0 00 1 1 1]The array element spacing was 0.5909 λ, and all of the numbers (MC) involved in the Monte Carlo experiments were 200. The noise added in the experiment is additive white Gaussian noise, the fast beat number is 64, and the number of points of all FFT is 128 points. In addition to experiment one, other experiments were performed with two targets and a taylor window was added. The comparison method mainly comprises an average mean square error (RMSE), and the calculation formula corresponding to the 2 targets is as follows:

experiment one: sparse array effective array element number (A) used in this experiment_rrNumber of 1 in) is 28, the directional pattern of the sparse array is compared with the directional pattern of 28 uniform linear arrays with an array element spacing of 0.5 lambda, and the result is shown in fig. 2. It can be seen that under the condition of the same (effective) array element, the sparse array (corresponding to red in the figure) can obtain a narrower main lobe, but the mean side lobe and the peak side lobe are both higher.

Experiment two: in order to compare the time complexity of FAC and RM, one-dimensional uniform linear arrays with array elements of 6-60 (interval of 1) are selected, the incidence directions of two targets are 20 degrees and 40 degrees respectively, and SNR is 20 dB. The results of the experiment are shown in FIG. 3. As can be seen from fig. 3, RM consumes less time when the number of array elements is less than 20, and FAC consumes less time when the number of array elements is greater than or equal to 20; it can also be seen that as the number of array elements increases, the time for RM increases rapidly, but the time for FAC increases very slowly. It can be shown that the time of the FAC method is insensitive to the number of array elements and always takes little time.

Experiment three: in order to verify the performance of FAC when the response of the strong target sidelobe is greater than that of the weak target, in this experiment, the SNRs of the two targets are respectively selected to be 20dB and 40dB, and the incident angles are respectively 10 ° and 30 °. The response map calculated by equation (7) is shown in fig. 4(a), and it can be seen that the maximum point corresponds to the target of 30 °, and the response corresponding to the target of 10 ° is not an extreme point, because the side lobe response brought by the target of 30 ° exceeds the response corresponding to the target of 10 °. The response for the 30 ° target (i.e., the second term in equation (13)) is shown in fig. 4(b), and fig. 4(c) is obtained by removing fig. 4(b) from fig. 4(a), and it can be seen that the response for the 30 ° target is well cleared and the peak for the 10 ° target appears. The FAC found results were: 10.031 ° and 29.999 °, the result of the RM calculation is: 10.044 ° and 29.946 °. The experiment shows that the FAC can still accurately estimate the incident angles of all targets under the condition that the sidelobe response of the strong target is larger than that of the weak target.

Experiment four: the two target angles were chosen to be 10 ° and 30 °, with equal SNR, varying from 10dB to 70dB, with 1dB separation, and the experimental results are shown in fig. 5. As can be seen from fig. 5, when the difference between the two target incident angles is large and the SNR is the same, the accuracy of FAC and RM is high, FAC is better than RM, and FAC and RM are not sensitive to SNR variation.

Experiment five: to verify the performance of the algorithm when the two targets have the same SNR and the angles are close, the SNR of both targets is selected to be 20dB, the incident angle of one target is fixed at 20 °, the incident angle of the other target is changed from 20.15 ° to 26 °, the interval is 0.1 °, and the experimental results are shown in fig. 6. As can be seen from fig. 6(a), when the SNR is the same and the two target incident angles are very close, the RM and FAC effect is relatively poor, the FAC effect is relatively good when the angles are very close, as the angle increases, the RM effect gradually becomes better, and when the angle difference is relatively large, the RM effect and FAC effect are both good.

In FIG. 6(b), the solid blue line (angle-1) and the broken line (angle-2) indicate the actual angles of the two targets, and the red and green indicate the angles obtained by FAC and RM, respectively. It can be seen that neither FAC nor RM is very accurate when the two target angles are close. When the two target angles are different greatly, the angles obtained by FAC and RM are very accurate.

Experiment six: to verify the performance of the algorithm when the two targets have different SNRs and the angles are close, the SNR of the first target is taken to be 20dB, the SNR of the second target is taken to be 25dB, the incident angle of the first target is fixed at 20 °, the incident angle of the second target is changed from 20.15 ° to 26 °, the interval is 0.1 °, and the experimental results are shown in fig. 7. As can be seen from fig. 7(a), when the SNR of the two targets is different, the FAC results are superior to the RM results in most cases. As can be seen from fig. 7(b), when the SNR of two targets is different, and the two target angles are relatively close, in most cases, the FAC method can estimate the angle with higher SNR almost exactly, and the value of the other angle is substantially consistent with that of RM estimation; while both angles of the RM estimate have large errors.

By comprehensively considering all simulation experiments, the method disclosed by the invention is low in time consumption, insensitive to array element number and high in target angle estimation precision, and can well inhibit the influence of sparse array strong target and high side lobe effect results on weak target angle estimation.

Claims

1. A sparse array DOA estimation method based on CLEAN is characterized by comprising the following steps:

step 2: t is>When 0, calculating the square accumulation result of the amplitude of all the snapshot data formed beamsOtherwise, ending the calculation process; wherein: y is_sIs as followss snapshot data x_sBeam data, y, formed using FFT_s＝FFT(x_s) (ii) a L is the number of fast beats;

Wherein p is₁Is in PThe beam number, p, corresponding to the maximum value₂The wave beam number is the second largest value, k is the amplitude comparison angle slope corresponding to the array, sign is the sign bit;

the above-mentioned

<math> <mrow> <mi>sign</mi> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mo>-</mo> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo><</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> <mo>,</mo> </mtd> <mtd> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>&GreaterEqual;</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math>

And 5: the target angle is calculated and the target angle is calculated,

2. The CLEAN-based sparse array direction of arrival DOA estimation method according to claim 1, characterized in that: the sparse array is formed by randomly removing some array elements in a uniformly spaced array by using an array A_rrAnd the element corresponding to the removed array element is 0, and the element corresponding to the reserved array element is 1.

3. The CLEAN-based sparse array direction of arrival DOA estimation method according to claim 1, characterized in that: the application of CLEAN idea to clear the detected target response is: all blocks calculated in step 2The amplitude square accumulation result P of the wave beam formed by the beat data is approximate to the amplitude square accumulation of the wave beam formed by the snapshot data, and firstly, the target T is obtained_mCorresponding amplitude

Wherein, P_m-1As a result of the (m) -1) th iteration, z_mIs P_m-1The beam number, theta, corresponding to the medium maximum value_mTarget T calculated for step (f)_mN is the number of array elements, k is 2 pi/λ;

at P_m-1Clearing the target T_mResponse to (2)